/// <summary>
/// Calculate a delaunay triangulation for the given enumeration of pixels.
/// </summary>
/// <typeparam name="T">The type of the pixels.</typeparam>
/// <param name="VoronoiFeatures">An enumeration of pixels of type T.</param>
/// <returns>An enumeration of triangles of type T.</returns>
public static IEnumerable<TriCircle> DelaunayTriangulation(this IEnumerable<VoronoiFeature> VoronoiFeatures)
{
#region Initial Checks
var _VoronoiFeatures = VoronoiFeatures.ToList();
var _NumberOfFeatures = _VoronoiFeatures.Count;
//if (_NumberOfFeatures < 3)
// throw new ArgumentException("Need at least three pixels for triangulation!");
var TriCircles = new List<TriCircle>();
#endregion
#region Set up the first triangle
var j = 0;
VoronoiFeature[] tri1;
TriCircle triangle = null;
do
{
tri1 = _VoronoiFeatures.Skip(j++).Take(3).ToArray();
triangle = new TriCircle(new GeoTriangle(tri1[0].GeoCoordinate, tri1[1].GeoCoordinate, tri1[2].GeoCoordinate));
}
while (triangle.Circle.Radius == 0);
TriCircles.Add(triangle);
_VoronoiFeatures = _VoronoiFeatures.Where(vf => !tri1.Contains(vf)).ToList();
#endregion
#region Include each point one at a time into the existing mesh
for (int i = 0; i < _VoronoiFeatures.Count; i++)
{
var Found = false;
#region The new voronoi feature lies inside an existing triangle
var TriCircleList = TriCircles.Where(TriCircle => TriCircle.Deleted == false).
OrderBy(TriCircle => TriCircle.Circle.Radius).ToArray();
foreach (var TriCircle in TriCircleList)
{
if (TriCircle.Triangle.Contains(_VoronoiFeatures[i].GeoCoordinate))
{
var Edges = new List<GeoLine>();
Edges.Add(new GeoLine(TriCircle.Triangle.P1, TriCircle.Triangle.P2));
Edges.Add(new GeoLine(TriCircle.Triangle.P2, TriCircle.Triangle.P3));
Edges.Add(new GeoLine(TriCircle.Triangle.P3, TriCircle.Triangle.P1));
// Add three new triangles for the current point
foreach (var _Edge in Edges)
TriCircles.Add(new TriCircle(new GeoTriangle(_Edge.P1, _Edge.P2, _VoronoiFeatures[i].GeoCoordinate)));
TriCircle.Deleted = true;
Found = true;
break;
}
}
#endregion
#region An external feature
if (!Found)
{
var PointList1 = (TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P1,
distance = TriCircle.Triangle.P1.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
}).
Union(
TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P2,
distance = TriCircle.Triangle.P2.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
})).
Union(
TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P3,
distance = TriCircle.Triangle.P3.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
}))).
OrderBy(agg => agg.distance).ToArray();
var PointList2 = PointList1.
Where(v =>
{
var newLine = new GeoLine(_VoronoiFeatures[i].GeoCoordinate, v.point);
foreach (var edges in TriCircles.Select(v2 => v2.Triangle.Borders))
{
foreach (var edge in edges)
{
if (edge.IntersectsWith(newLine, false, true))
{
return false;
}
}
}
return true;
}).
ToArray();
TriCircles.Add(new TriCircle(new GeoTriangle(PointList2[0].point, PointList2[1].point, _VoronoiFeatures[i].GeoCoordinate)));
}
#endregion
}
#endregion
return TriCircles.Where(tc => tc.Deleted == false);//.Select(tc => tc.Triangle);
}
/// <summary>
/// Calculate a delaunay triangulation for the given enumeration of pixels.
/// </summary>
/// <typeparam name="T">The type of the pixels.</typeparam>
/// <param name="VoronoiFeatures">An enumeration of pixels of type T.</param>
/// <returns>An enumeration of triangles of type T.</returns>
public static IEnumerable <TriCircle> DelaunayTriangulation(this IEnumerable <VoronoiFeature> VoronoiFeatures)
{
#region Initial Checks
var _VoronoiFeatures = VoronoiFeatures.ToList();
var _NumberOfFeatures = _VoronoiFeatures.Count;
//if (_NumberOfFeatures < 3)
// throw new ArgumentException("Need at least three pixels for triangulation!");
var TriCircles = new List <TriCircle>();
#endregion
#region Set up the first triangle
var j = 0;
VoronoiFeature[] tri1;
TriCircle triangle = null;
do
{
tri1 = _VoronoiFeatures.Skip(j++).Take(3).ToArray();
triangle = new TriCircle(new GeoTriangle(tri1[0].GeoCoordinate, tri1[1].GeoCoordinate, tri1[2].GeoCoordinate));
}while (triangle.Circle.Radius == 0);
TriCircles.Add(triangle);
_VoronoiFeatures = _VoronoiFeatures.Where(vf => !tri1.Contains(vf)).ToList();
#endregion
#region Include each point one at a time into the existing mesh
for (int i = 0; i < _VoronoiFeatures.Count; i++)
{
var Found = false;
#region The new voronoi feature lies inside an existing triangle
var TriCircleList = TriCircles.Where(TriCircle => TriCircle.Deleted == false).
OrderBy(TriCircle => TriCircle.Circle.Radius).ToArray();
foreach (var TriCircle in TriCircleList)
{
if (TriCircle.Triangle.Contains(_VoronoiFeatures[i].GeoCoordinate))
{
var Edges = new List <GeoLine>();
Edges.Add(new GeoLine(TriCircle.Triangle.P1, TriCircle.Triangle.P2));
Edges.Add(new GeoLine(TriCircle.Triangle.P2, TriCircle.Triangle.P3));
Edges.Add(new GeoLine(TriCircle.Triangle.P3, TriCircle.Triangle.P1));
// Add three new triangles for the current point
foreach (var _Edge in Edges)
{
TriCircles.Add(new TriCircle(new GeoTriangle(_Edge.P1, _Edge.P2, _VoronoiFeatures[i].GeoCoordinate)));
}
TriCircle.Deleted = true;
Found = true;
break;
}
}
#endregion
#region An external feature
if (!Found)
{
var PointList1 = (TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P1,
distance = TriCircle.Triangle.P1.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
}).
Union(
TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P2,
distance = TriCircle.Triangle.P2.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
})).
Union(
TriCircles.Select(TriCircle => new
{
point = TriCircle.Triangle.P3,
distance = TriCircle.Triangle.P3.DistanceTo(_VoronoiFeatures[i].GeoCoordinate)
}))).
OrderBy(agg => agg.distance).ToArray();
var PointList2 = PointList1.
Where(v =>
{
var newLine = new GeoLine(_VoronoiFeatures[i].GeoCoordinate, v.point);
foreach (var edges in TriCircles.Select(v2 => v2.Triangle.Borders))
{
foreach (var edge in edges)
{
if (edge.IntersectsWith(newLine, false, true))
{
return(false);
}
}
}
return(true);
}).
ToArray();
TriCircles.Add(new TriCircle(new GeoTriangle(PointList2[0].point, PointList2[1].point, _VoronoiFeatures[i].GeoCoordinate)));
}
#endregion
}
#endregion
return(TriCircles.Where(tc => tc.Deleted == false));//.Select(tc => tc.Triangle);
}
